Wireframe horizontal vertices - retro video game effect
In your Wireframe Modifier, uncheck Replace Original. Up the Material: value to 1.

Go to the Materials tab. Make sure you have two material slots, the top being black and the bottom being green.

This will make it so that you have something black in between the green lines to stop light from the hidden green lines getting through.

Jimmy Gunawan's image; cropped and modified:



Blender Nerd's image from his YouTube video; cropped:



A gif I created:



Check out the gif's .blend file!